Asked by Jenna Garland on Jul 11, 2024
Verified
A quality control manager at a bottling plant wishes to know if the median amount of juice in their 473 mL bottles actually falls below 473 mL.The amounts of juice in 24 randomly selected juice bottles are measured.Of the 24 bottles,14 contained less than 473 mL and 10 contained more 473 mL.Perform a sign test to determine if the median amount is less than 473 mL.Use a 10% level of significance.
Sign Test
A non-parametric test used to determine if there is a significant difference between the median of two related samples.
Median Amount
The middle value in a set of numbers, which divides the set into two equal halves.
Level Of Significance
A threshold chosen by the researcher which denotes the probability below which a null hypothesis is rejected, indicating statistical significance.
- Understand the concept and application of the sign test for median.
- Learn how to perform statistical analysis using real-life scenarios.
- Be able to determine the significance level and its implications in hypothesis testing.
Verified Answer
KC
Keyhoon ChungJul 16, 2024
Final Answer :
H0: The median amount per bottle is 473 mL.That is,the true proportion of bottles containing less than 473 mL is 0.50.HA: The true proportion of bottles containing less than 473 mL is more than 0.50.That is,p0 > 0.50.z = 0.81.p-value = 0.2090.Fail to reject H0.
Learning Objectives
- Understand the concept and application of the sign test for median.
- Learn how to perform statistical analysis using real-life scenarios.
- Be able to determine the significance level and its implications in hypothesis testing.